• Proceedings of the KSR Conference
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• 2007.11a
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• pp.585-594
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• 2007

This paper presents the methods which estimate the influence of ground subsidence and the stability of buildings by tunnel excavation in urban area. First, we study the behaviour of ground subsidence using neural network and numerical method. And we analyze the characteristic of both methods. Using the both methods, we evaluate the stability of buildings by subway tunnel excavation and we compare the results of the neural network and numerical analysis.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.23 no.8
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• pp.734-741
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• 2013

In contrast of external excitations, parametric excitations can produce a large response when the excitation frequency is away from the linear natural frequencies. The Mathieu equation is the simplest differential equation with periodic coefficients, which lead to the parametric excitation. The Mathieu equation may have the unbounded solutions. This work conducted the stability analysis for the Mathieu equation, using Floquet theory and numerical method. Using Lindstedt's perturbation method, harmonic solutions of the Mathieu equation and transition curves separating stable from unstable motions were obtained. Using Floquet theory with numerical method, stable and unstable regions were calculated. The numerical method had the same transition curves as the perturbation method. Increased stable regions due to the inclusion of damping were calculated.

• Smart Structures and Systems
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• v.25 no.6
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• pp.719-732
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• 2020

Real-time hybrid simulation (RTHS) which combines physical experiment with numerical simulation is an advanced method to investigate dynamic responses of structures subjected to earthquake excitation. The desired displacement computed from the numerical substructure is applied to the experimental substructure by a servo-hydraulic actuator in real time. However, the magnitude decay and phase delay resulted from the dynamics of the servo-hydraulic system affect the accuracy and stability of a RTHS. In this study, a robust stability analysis procedure for a general single-degree-of-freedom structure is proposed which considers the uncertainty of servo-hydraulic system dynamics. For discussion purposes, the experimental substructure is a portion of the entire structure in terms of a ratio of stiffness, mass, and damping, respectively. The dynamics of the servo-hydraulic system is represented by a multiplicative uncertainty model which is based on a nominal system and a weight function. The nominal system can be obtained by conducting system identification prior to the RTHS. A first-order weight function formulation is proposed which needs to cover the worst possible uncertainty envelope over the frequency range of interest. Then, the Nyquist plot of the perturbed system is adopted to determine the robust stability margin of the RTHS. In addition, three common delay compensation methods are applied to the RTHS loop to investigate the effect of delay compensation on the robust stability. Numerical simulation and experimental validation results indicate that the proposed procedure is able to obtain a robust stability margin in terms of mass, damping, and stiffness ratio which provides a simple and conservative approach to assess the stability of a RTHS before it is conducted.

• Bulletin of the Korean Mathematical Society
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• v.47 no.6
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• pp.1225-1234
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• 2010

Numerical solutions for the fractional differential dispersion equations with nonlinear forcing terms are considered. The backward Euler finite difference scheme is applied in order to obtain numerical solutions for the equation. Existence and stability of the approximate solutions are carried out by using the right shifted Grunwald formula for the fractional derivative term in the spatial direction. Error estimate of order $O({\Delta}x+{\Delta}t)$ is obtained in the discrete $L_2$ norm. The method is applied to a linear fractional dispersion equations in order to see the theoretical order of convergence. Numerical results for a nonlinear problem show that the numerical solution approach the solution of classical diffusion equation as fractional order approaches 2.

• Structural Engineering and Mechanics
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• v.85 no.2
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• pp.207-216
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• 2023

Three time-discontinuous Galerkin quadrature element methods (TDGQEMs) are developed for structural dynamic problems. The weak-form time-discontinuous Galerkin (TDG) statements, which are capable of capturing possible displacement and/or velocity discontinuities, are employed to formulate the three types of quadrature elements, i.e., single-field, single-field/least-squares and two-field. Gauss-Lobatto quadrature rule and the differential quadrature analog are used to turn the weak-form TDG statements into a system of algebraic equations. The stability, accuracy and numerical dissipation and dispersion properties of the formulated elements are examined. It is found that all the elements are unconditionally stable, the order of accuracy is equal to two times the element order minus one or two times the element order, and the high-order elements possess desired high numerical dissipation in the high-frequency domain and low numerical dissipation and dispersion in the low-frequency domain. Three fundamental numerical examples are investigated to demonstrate the effectiveness and high accuracy of the elements, as compared with the commonly used time integration schemes.

• Tunnel and Underground Space
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• v.10 no.3
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• pp.441-446
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• 2000

Numerical analysis using FLAC3D has been conducted to estimate the stability of a large underground hall that is to be excavated in a mined area and constructed as an unit of a resort park. Numerical modelling is divided into two stages. The first stage is related to the analysis of the mechanical stability of the hall itself and the second to that of the influence of an adjacent mined cavity upon the hall. In the first stage, the stability of the hall is judged from the interpretation of numerical results in three respects: convergence of the unbalanced force of the model, occurrence of plastic zones and distribution of the displacement. In the second stage, variation of the stress state around the underground hall due to the existence of the cavity is compared to that in the case of the absence of the cavity. Through these analyses, it could be known that the large underground hall is not exposed to any mechanical problems and also not affected by the adjacent cavity.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.39 no.9
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• pp.805-815
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• 2011

Nonlinear Parabolized Stability Equations(NSPE) can be effectively used to study more throughly the transition process. NPSE can efficiently analyze the stability of a nonlinear region in transition process with low computational cost compared to Direct Numerical Simulation(DNS). In this study, NPSE in general coordinate system is formulated and a computer code to solve numerically the equations is developed. Benchmark problems for incompressible and compressible boundary layers over a flat plate are analyzed to validate the present code. It is confirmed that the NPSE methodology constructed in this study is an efficient and effective tool for nonlinear stability analysis.

• Tunnel and Underground Space
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• v.18 no.4
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• pp.243-251
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• 2008

Recently, the mining methods are changing from surface mining to underground mining because of the increment of the environmental issues and legal regulations. Therefore, the stability of underground openings is a major concern for the safety and productivity of mining operations. In this paper, a survey of structural geology and discontinuities were carried out at a limestone mine. The relevant mechanical properties of rocks were determined by the laboratory tests and rock mass classifications (RMR and Q-system) for the mine design and input data for the stability analysis. The dimensions of unsupported span for underground openings and pillar were decided based on the RMR values of rock mass classifications. The stability analysis for the suggested mine design was examined through the empirical methods (stability graph method and critical span curve) and 3-D numerical analysis (Visual-FEA).

• Journal of Korean Tunnelling and Underground Space Association
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• v.12 no.5
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• pp.389-397
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• 2010

This paper presents the effects of the tunnel stability using rebar steel pipe which is the steel pipe reinforced by rebar. In order to carry out this research, not only the theoretical and experimental study for bending stiffness of normal steel pipes and rebar steel pipes but also numerical analysis of tunnel stability are performed. It is clearly found from the results that 65% of bending stiffness of the rebar steel pipe is larger than that of the normal steel pipe. The results obtained from the numerical analysis of tunnel stability show that about 10% of tunnel stability is increased in case of the rebar steel pipe. The rebar steel pipe, therefore, may be very useful to develope the tunnel stability economically.

• Geomechanics and Engineering
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• v.32 no.3
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• pp.245-254
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• 2023

Through qualitative analysis and quantitative analysis, the contradictory conclusions about the stability of the settled goaf with two-layer coal seams subject to building load were obtained. Therefore, it is necessary to combine the additional stress method and numerical simulation to further analyze the foundation stability. Through borehole analysis and empirical formula analogy, the height of water-conducting fracture zone in No.4 coal and No.9 coal were obtained, providing the calculation range of water-conducting fracture zone for numerical simulation. To ensure the accuracy of the elastic modulus of broken gangue, the stress-strain curve were obtained by broken gangue compression test in dried state of No.4 coal seam and in soaking state of No.9 coal seam. To ensure the rationality of the numerical simulation results, the actual measured subsidence data were retrieved by numerical simulation. FISH language was used to analyze the maximum building load on the surface and determine the influence depth of building load on the foundation. The critical building load was 0.16 MPa of No.4 settled goaf and was 1.6 MPa of No.9 settled goaf. The additional stress affected the water-conducting fracture zone obviously, resulted in the subsidence of water-conducting fracture zone was greater than that of bending subsidence zone. In this paper, the additional stress method was analyzed by numerical simulation method, which can provide a new analysis method for the treatment and utilization of the settled goaf.